Provably positive high-order schemes for ideal magnetohydrodynamics: analysis on general meshes

Entropy stable high order discontinuous Galerkin methods for ideal compressible MHD on structured meshes

(2018) Yong Liu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Ideal GLM-MHD: About the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations

(2018) Dominik Derigs et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Globally Divergence-Free Discontinuous Galerkin Methods for Ideal Magnetohydrodynamic Equations

(2018) Pei Fu et al.   JOURNAL OF SCIENTIFIC COMPUTING

Positivity-Preserving Analysis of Numerical Schemes for Ideal Magnetohydrodynamics

(2018) Kailiang Wu   SIAM JOURNAL ON NUMERICAL ANALYSIS

Runge–Kutta discontinuous Galerkin methods for the special relativistic magnetohydrodynamics

(2017) Jian Zhao et al.   JOURNAL OF COMPUTATIONAL PHYSICS

On positivity-preserving high order discontinuous Galerkin schemes for compressible Navier–Stokes equations

(2017) Xiangxiong Zhang   JOURNAL OF COMPUTATIONAL PHYSICS

Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations

(2017) Kailiang Wu et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Divergence-Free WENO Reconstruction-Based Finite Volume Scheme for Solving Ideal MHD Equations on Triangular Meshes

(2016) Zhiliang Xu et al.   Communications in Computational Physics

Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part II: The two-dimensional case

(2016) François Vilar et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A high-order positivity-preserving single-stage single-step method for the ideal magnetohydrodynamic equations

(2016) Andrew J. Christlieb et al.   JOURNAL OF COMPUTATIONAL PHYSICS

New central and central discontinuous Galerkin schemes on overlapping cells of unstructured grids for solving ideal magnetohydrodynamic equations with globally divergence-free magnetic field

(2016) Zhiliang Xu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Entropy Stable Finite Volume Scheme for Ideal Compressible MHD on 2-D Cartesian Meshes

(2016) Praveen Chandrashekar et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

High order parametrized maximum-principle-preserving and positivity-preserving WENO schemes on unstructured meshes

(2015) Andrew J. Christlieb et al.   JOURNAL OF COMPUTATIONAL PHYSICS

High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics

(2015) Kailiang Wu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Parametrized Positivity Preserving Flux Limiters for the High Order Finite Difference WENO Scheme Solving Compressible Euler Equations

(2015) Tao Xiong et al.   JOURNAL OF SCIENTIFIC COMPUTING

An Explicit High-Order Single-Stage Single-Step Positivity-Preserving Finite Difference WENO Method for the Compressible Euler Equations

(2015) David C. Seal et al.   JOURNAL OF SCIENTIFIC COMPUTING

Positivity-Preserving Finite Difference Weighted ENO Schemes with Constrained Transport for Ideal Magnetohydrodynamic Equations

(2015) Andrew J. Christlieb et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Finite difference weighted essentially non-oscillatory schemes with constrained transport for ideal magnetohydrodynamics

(2014) Andrew J. Christlieb et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Positivity-preserving DG and central DG methods for ideal MHD equations

(2013) Yue Cheng et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Positivity-preserving method for high-order conservative schemes solving compressible Euler equations

(2013) Xiangyu Y. Hu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Multidimensional HLLC Riemann solver for unstructured meshes – With application to Euler and MHD flows

(2013) Dinshaw S. Balsara et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Parametrized Maximum Principle Preserving Flux Limiters for High Order Schemes Solving Multi-Dimensional Scalar Hyperbolic Conservation Laws

(2013) Chao Liang et al.   JOURNAL OF SCIENTIFIC COMPUTING

Parametrized maximum principle preserving flux limiters for high order schemes solving hyperbolic conservation laws: one-dimensional scalar problem

(2013) Zhengfu Xu   MATHEMATICS OF COMPUTATION

Self-adjusting, positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics

(2012) Dinshaw S. Balsara   JOURNAL OF COMPUTATIONAL PHYSICS

Locally divergence-free central discontinuous Galerkin methods for ideal MHD equations

(2012) Sergey Yakovlev et al.   Journal of Computational Science

Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergence-free magnetic field

(2011) Fengyan Li et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A robust numerical scheme for highly compressible magnetohydrodynamics: Nonlinear stability, implementation and tests

(2011) K. Waagan et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Maximum-Principle-Satisfying and Positivity-Preserving High Order Discontinuous Galerkin Schemes for Conservation Laws on Triangular Meshes

(2011) Xiangxiong Zhang et al.   JOURNAL OF SCIENTIFIC COMPUTING

Approximate Riemann Solvers and Robust High-Order Finite Volume Schemes for Multi-Dimensional Ideal MHD Equations

(2010) Franz Georg Fuchs et al.   Communications in Computational Physics

On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes

(2010) Xiangxiong Zhang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

On maximum-principle-satisfying high order schemes for scalar conservation laws

(2010) Xiangxiong Zhang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms

(2010) Xiangxiong Zhang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A multiwave approximate Riemann solver for ideal MHD based on relaxation II: numerical implementation with 3 and 5 waves

(2010) François Bouchut et al.   NUMERISCHE MATHEMATIK

A positive MUSCL-Hancock scheme for ideal magnetohydrodynamics

(2009) K. Waagan   JOURNAL OF COMPUTATIONAL PHYSICS

Multidimensional HLLE Riemann solver: Application to Euler and magnetohydrodynamic flows

(2009) Dinshaw S. Balsara   JOURNAL OF COMPUTATIONAL PHYSICS

High Order Strong Stability Preserving Time Discretizations

(2008) Sigal Gottlieb et al.   JOURNAL OF SCIENTIFIC COMPUTING

Increasing the accuracy in locally divergence-preserving finite volume schemes for MHD

(2007) Robert Artebrant et al.   JOURNAL OF COMPUTATIONAL PHYSICS